Download A regular period for Saturn’s magnetic field that G. Giampieri

Vol 441|4 May 2006|doi:10.1038/nature04750
LETTERS
A regular period for Saturn’s magnetic field that
may track its internal rotation
G. Giampieri1, M. K. Dougherty2, E. J. Smith1 & C. T. Russell3
The rotation rate of a planet is one of its fundamental properties.
Saturn’s rotation, however, is difficult to determine because there
is no solid surface from which to time it, and the alternative
‘clock’—the magnetic field—is nearly symmetrically aligned with
the rotation axis1–7. Radio emissions, thought to provide a proxy
measure of the rotation of the magnetic field, have yielded
estimates of the rotation period between 10 h 39 min 22 s and
10 h 45 min 45 s (refs 8–10). Because the period determined from
radio measurements exhibits large time variations, even on timescales of months, it has been uncertain whether the radio-emission
periodicity coincides with the inner rotation rate of the planet.
Here we report magnetic field measurements that revealed a timestationary magnetic signal with a period of 10 h 47 min 6 s 6 40 s.
The signal appears to be stable in period, amplitude and phase
over 14 months of observations, pointing to a close connection
with the conductive region inside the planet, although its
interpretation as the ‘true’ inner rotation period is still uncertain.
A fundamental question concerning Saturn’s interior remains
unanswered despite measurements spanning a quarter of a century:
what is the rotation rate of the deep interior? This is different from
the case of Jupiter, where the internal rotation rate can be accurately
measured thanks to the presence of a significant dipole tilt11. In
Saturn’s case, where the magnetic field is highly axially symmetric, we
have a dilemma: we need a clear azimuthal field component in order
to measure the rotation rate of the planet, but in order to be able to
invert the data to find the azimuthal field we need to know the
rotation rate quite accurately, or else the azimuthal component will
be averaged to zero. Periodic modulations in the magnetic field
components that may be associated with the rotation of Saturn’s
interior were first found in the Pioneer 11 data, although a careful
analysis of the 10.5-h periodicity observed seemed to rule out an
internal origin12. These periodic azimuthal signals continue to be
intriguing because they hold promise of providing the necessary
‘clock’ to time Saturn’s rotational period.
The lack of a significant azimuthal field of internal origin in
Saturn’s magnetic field has yet to be explained, and several planetary
models have been proposed to account for it. The most notable is
from Stevenson13, who proposed that the presence of a conductive
shell, external to the dynamo region and differentially rotating with
respect to it, can greatly suppress the non-axisymmetric components
of the internal field away from the planet. In addition, data from the
Pioneer and Voyager fly-bys were reanalysed using modern inversion
techniques and without any a priori assumption about the symmetry
of the internal field14. This analysis revealed the possible existence of
some non-axisymmetric field, although the limited spatial sampling
of the three fly-bys did not allow an unambiguous measurement of
the higher-order components of the field to be made.
Recently, Cassini orbiter observations have greatly extended the
in situ set of magnetic field observations at Saturn7. We have analysed
magnetic field data collected by the fluxgate magnetometer on board
Cassini between Saturn orbit insertion (SOI, July 2004) and orbit 13
(August 2005), during which time the spacecraft flew by the planet on
15 separate occasions. The closest approach distance for these passes
varies between 1.33R S and 6.19R S (1R S ¼ 60,268 km is defined as
Saturn’s planetary radius)15, and the data used were ten-minute
averages inside 10R S. Best-fit parameters of an axially symmetric
planetary field (up to octupole terms) and of an axially symmetric
ring current field16,17 were derived, and a search for periodic modulations in the resulting residuals was carried out. The residuals of the
three magnetic field components in a spherical polar co-ordinate
system (B r, B v, B f) can be seen in Fig. 1a–c respectively. The residuals
reveal a clear periodic signature in all three of the components but
most clearly in the azimuthal one (Fig. 1c), which is not affected at all
Figure 1 | Periodicity in Saturn’s magnetic field. a–c, The spherical
components of the magnetic field residuals (a, B r ; b, B v ; c, B f) in the IAU
reference frame. The vertical dashed lines separate the different passes,
indicated in the top panel (from SOI to orbit 13). These residuals are
calculated by subtracting the estimated contribution of the internal
planetary field and the external magnetodisk current sheet. For each pass,
best fit parameters of an axially symmetric magnetodisk field were derived.
The magnetodisk parameters were assumed to respond to the time varying
magnetospheric conditions, and therefore allowed to vary from pass to pass.
In addition, the internal planetary field was estimated using standard
inversion techniques on the entire sequence of observations. In order not to
interfere with our search for periodic signatures in the data, the planetary
field was assumed to be axisymmetric.
1
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA. 2The Blackett Laboratory, Imperial College London, London SW7 2AZ, UK. 3UCLA
Institute of Geophysics and Planetary Physics, Los Angeles, California 90025, USA.
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NATURE|Vol 441|4 May 2006
by the removal of axisymmetric contributions from the magnetodisk
and the internal field. This signal can allow the first accurate and
direct measurement of the magnetic field periodicity.
A difficulty we face when searching for periodicities in time series
data such as that in Fig. 1 is that the spacecraft is constantly moving
with respect to the planet. This introduces a Doppler-like effect on
the magnetic field, which is rotating with the planet; in particular,
because Cassini is moving in the same sense as the planet rotates, the
field is shifted towards longer periods. This effect, which is accumulated over many months and orbits of the planet, could make it
impossible to determine the actual frequency of the periodic signal,
whatever its origin. In order to remove this effect, we replace the
actual physical time (t) of the observation with a ‘longitudinal’ time,
which we define as t ¼ 2fP/(2p), where f is the IAU longitude of
the spacecraft, and P is the IAU rotation period of Saturn (defined as
P ¼ 10 h 39 min 22.4 s; see ref. 18 for the definition of Saturn’s IAU
cartographic coordinates). The minus sign in the definition assures
that t is monotonically increasing, apart from a very short interval
around closest approach during SOI when Cassini’s velocity was
larger than Saturn’s angular velocity. The implication is that when
Cassini is in a fixed position in inertial space, f ¼ 22pt/P and t ¼ t.
In general though, because of the orbital motion of the spacecraft,
t # t. In such a scenario, a magnetic feature corotating with the
planet would appear as a sinusoidal signal, which is proportional to
exp(i2pt/P), independent of the spacecraft motion.
In addition, because we limit our analysis to data within the inner
and middle magnetosphere, our observational time sequence contains data gaps that often last for many weeks. This makes the use of
standard fast Fourier transform techniques impractical, and instead
we use the Lomb-Scargle algorithm, which facilitates the analysis of
unevenly spaced data19. Applying this spectral technique to the
residual data in Fig. 1 produces the power spectra shown in Fig. 2.
A very clear peak can be seen in all three of the components at
P ¼ 10 h 47 min 6 s ^ 40 s. No other peaks of this significance were
found outside the plotted range. A series of side lobes extends on
either side of the main peak, associated with an amplitude modulation of the signal due to Cassini’s orbital motion. We can estimate
an uncertainty of j P ¼ 40 s for this period from the half-width of the
Figure 2 | Normalized spectra of the magnetic field residuals. a–c, The
power spectra of the residuals from Fig. 1; the vertical red line indicates the
IAU rotation period being used to date. No component at the IAU rotation
period can be seen, whereas a peak at 10 h 47 min 6 s is clearly visible. Note
the side lobes of the rotation peak, associated with the orbital period of
Cassini. The width of the rotation peak, mainly due to the finite duration of
the data record, limits the intrinsic time variation of the period to within
40 s.
peak in the spectrum. A simple inspection of the field components in
the time domain reveals that the phase of the periodic signal varies by
less than 0.58 from orbit to orbit.
Can this periodic signal be a direct signature of Saturn’s rotation
rate? If we accept that the radio emission period is related to the
rotation rate of the planetary interior, then the implication is that
the rotation of the planet has slowed down by several minutes over a
25-year period. Such a situation would require either a large external
torque or a large redistribution in the internal density and velocity
profiles, both unrealistic scenarios, because the dissipated energy
(,1030 erg s21, under simple assumptions) would be a million times
the planet’s luminosity13. We must then conclude that the period
measured in the radio emission is modulated by external effects. For
example, the solar wind may cause the observed varying phase
modulation of the radio source20. On the other hand, the magnetic
field signal, which we have only studied over the much shorter time
span of the Cassini mission, shows no obvious variations in period,
phase or amplitude, and can well be used to define an improved
rotation rate of the planetary source. In this case, one should rescale
the planetary longitude accordingly. In fact, only when the zero
longitude axis is redefined by taking into account the new rotation
period, are magnetic field observations, taken at the same longitude
but at different epochs, found to overlap, as one would expect from
an internal source.
The simplest model that produces a periodic field is the tilted
dipole, but if this were the source of the periodic signal we would see
associated changes that are not observed. More precisely, to generate
a sinusoidal modulation proportional to cosf in the internal field,
non-zero azimuthal terms of degree 1 are required in the magnetic
field potential that depend on the other two spherical coordinates
(r, v), and no such latitudinal or radial dependence is observed in the
residuals in Fig. 1. To see this more clearly, we show an example of the
expected B f component, which would arise from a hypothetical
tilted dipole (Fig. 3). This azimuthal field is very different from that
which we observe. We conclude that a low-order non-axisymmetric
Figure 3 | Comparison with a tilted dipole signal. The expected azimuthal
field arising from a tilted dipole is shown by the thin green curve, and is
compared to the real data, in red, for orbit B through to orbit 9. Also shown
is a sinusoid of period 10 h 47 min 6 s with a constant phase (blue dashed
line). Note how the expected dipole signal is in phase with the azimuthal
component of the magnetic field, thanks to the re-definition of the longitude
from Cassini data. However, the increase in field values near closest
approach cannot be found in the data itself. The assumed equatorial
component of the dipole has a magnitude of 825 nT in the direction of 2768.
As in Fig. 1, the vertical dashed lines separate the orbits.
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NATURE|Vol 441|4 May 2006
internal field cannot be responsible for the large amplitude modulation shown in Fig. 1.
We note that local spin-periodic magnetic field perturbations
observed in some of the Pioneer and Voyager data were explained
via a ‘camshaft’ model, which proposed that a hypothetical anomaly
(possibly magnetic or atmospheric) could generate periodic waves in
the magnetosphere21. At present, we are looking at the polarization
results from Cassini data in order to be able to confirm whether this
hypothesis is able to explain the observed periodicity. We are left with
the conundrum that we have a magnetic signal that appears to be
stable in period, thus suggesting that it is linked to the rotation of the
interior, but we do not yet know how that signal is produced.
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Acknowledgements Results presented here represent one aspect of research
carried out at the Jet Propulsion Laboratory, California Institute of Technology,
under contract with the National Aeronautics and Space Administration. This
research was performed while G.G. held a National Research Council senior
research associateship award at JPL. We thank M. E. Burton and J. Wolf for
suggestions on the manuscript.
Author Information Reprints and permissions information is available at
npg.nature.com/reprintsandpermissions. The authors declare no competing
financial interests. Correspondence and requests for materials should be
addressed to G.G. ([email protected]).
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